The signal device I saw in advertisements, costs over a thousand dollars. A no-frills cell phone is around $20 and a calling card every few months, another $20.
I imigine a Clapper could be re-wired for alarms. "Clap on. Clap off. Clap on clap off Clap on..."
True, as long as she's in cell range and wears the phone around her neck. A phone on a counter several feet away would not have helped her in this case. She needs people with keys that can check on her, and do... every day.